Find all numbers c that satisfy the conclusion of Rolle's Theorem.  f(x) = x^3 − x^2 − 2x + 8     interval= [0, 2]

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cosinusix | College Teacher | (Level 3) Assistant Educator

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f is continuous, and differentiable on [0,2].

therefore by Rolle's Theorem, `EEc in(0,2) | f'(c)=0`


Let's find c.


using the quadratic formula `f'(x)=0` iff `x=(2+-sqrt(4+4*3*2))/(6)`


Since `c in(0,2)` , `c=(1+sqrt(7))/3`